To measure distances in **angular degrees** between two stars
or planets, or between any star and the horizon. **Quadrants** can
measure from 0 to 90 degrees; **sextants** from 0 to 60 degrees; a
protractor from 0 to 180 degrees (which is like having a
double-quadrant).

There is no way to measure the actual distance between stars in space with a quadrant. All that is determined is the apparent angular separation in degrees. For example, what is the angular distance between the horizon and the zenith (the point directly overhead)? From your answer to this question you can infer why a quadrant is a convenient size for this kind of instrument (we will never need to use both sides of the protractor at the same time; all our measurements will be 90 degrees or less).

For clarity, measurements in angular degrees are sometimes referred to as measurements of arc, meaning that they are measurements along an arc or circumference of a great circle. Units of arc measurement include degrees, minutes, and seconds:

- 1 angular degree = 60
**minutes**of arc - 1 arc minute = 60
**seconds**of arc - How many seconds of arc are contained in one angular degree?

Tycho Brahe's **mural quadrant** is a famous example of his
large and extremely precise astronomical instruments. Sightings were
made through a hole at the upper left in the south-facing wall.
(Picture to be added soon!)

Construct your own quadrant using an ordinary plastic protractor:

- For best results use the protractor manufactured by Eiskars with a plastic pivot arm, sold in the OBU Bookstore.
- Notice the shaded rectangular region that runs along the right edge of the rotating arm in the illustration above. This is a strip cut from a 3x5 note card (or equivalent stiff paper) bent lengthwise by 90 degrees. It functions as a sighting device.
- To construct the bent-card sighting device do the following:
- Cut card material into a rectangle about 0.5 x 3.5 inches.
- Fold it in half lengthwise and work with it until it retains a 90 degree bend.
- Align the creased edge of the card with the bottom edge of the protractor arm.
- Slide the card lengthwise on the protractor arm until the edge of one of its ends is located at the midpoint of the circular hole that forms the pivot where the protractor arm is attached (this pivot allows the protractor arm to rotate all the way around). As you look down at the folded paper card as it overlaps the circular pivot hole, this end of the card should cover up to 1/4th of the total area of the circle, with its folded corner located precisely at the center of the circular hole (see illustration).
- Tape the sighting device to the rotating arm as illustrated.

- Set the protractor arm at zero degrees by the following means.
- Slide your thumb's fingernail on the top surface of the protractor until it runs into the raised zero mark (you should be able to feel it in the dark).
- Orient your fingernail so that it is perpendicular to the protractor.
- Move the arm of the protractor until it hits your fingernail.
- Verify this zero-setting by flashlight until you acquire sufficient confidence through practice.

- Look along the arm sighting device directly at the first star or other celestial object.
- Without moving the protractor as a whole, rotate the protractor arm until it is roughly pointed toward the 2nd celestial object .
- Carefully move your head, without moving the protractor, so that you can sight the 2nd celestial object along the arm sighting device.
- Once you are satisfied with this 2nd alignment, you can relax, lower the protractor, turn on your flashlight, and read off the angular measurement indicated by the arm.

- Hold the protractor as level as possible so that your true
horizon (not treetops or hill tops) will be at zero degrees. (This
is the same as making your first sighting in the previous method.)
- Does the height of the protractor above the ground matter? Will you get different results if you hold your protractor horizontally at eye level, horizontally at waist level, or horizontally above your head? Can you change its height at will without affecting your results? Why?

- Without changing the orientation of the protractor as a whole, rotate the protractor arm until it is pointed roughly toward the celestial object whose altitude is in question (this is analogous to making your "2nd sighting" in the previous method).
- Carefully move your head (without moving the protractor) so that you can sight the celestial object along the sighting device.
- Once you are satisfied with this alignment, you can relax, turn on your flashlight, and read off the angular measurement indicated by the arm. This measurement is the altitude of the celestial object.